Superconducting electromagnet apparatus

ABSTRACT

A superconducting electromagnet apparatus comprises a main coil assembly ( 1 ) and a main current supply ( 5 ) energising and de-energising the main coil assembly ( 1 ), and for persisting the current flow in the main coil assembly ( 1 ) when a desired constant current level has been reached, in order to generate a central magnetic field of high homogeneity in a working volume. The apparatus further comprises a B 0  shim coil assembly ( 2 ) comprising superconducting shim coils connected within a closed loop and arranged to magnetically couple with the main coil assembly ( 1 ) and an auxiliary current supply ( 6 ) for supplying current to the closed loop, and for persisting the current flow in the closed loop when a desired constant current level has been reached, in order to provide fine adjustment of the central magnetic field within the working volume without significantly degrading the homogeneity of the central magnetic field. A control circuit ( 31, 38 ) is provided for controlling the main and auxiliary current supplies ( 5, 6 ) and the main coil assembly ( 1 ), the B 0  shim coil assembly ( 2 ) and the control circuit ( 31, 38 ) are adapted to at least partly compensate for the effect of variation of the magnetic field within the working volume with time. In this case the shim coil assembly performs both the function of a B 0  shim and at the same time compensates for the effect of variation of the magnetic field within the working volume with time, thus avoiding the need to provide individual closed loop coil assemblies for performing these functions separately which would result in functional difficulties due to inductive coupling between these auxiliary coil assemblies.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to superconducting electromagnet apparatus. Suchapparatus can be used in various applications including nuclear magneticresonance (NMR) spectroscopy and imaging and Fourier-transform massspectrometry (FTMS).

2. Description of the Related Art Including Information Disclosed Under37 CFR 1.97 and 1.98

In conventional superconducting electromagnet apparatus a mainsuperconducting coil assembly of cylindrical form is used to produce acentral magnetic field which varies very little over a specified workingvolume within the bore of the cylinder, that is the so-calledhomogeneity volume. In many applications of such apparatus, it isnecessary for a precise value of the central magnetic field to be set.Furthermore it is often necessary or desirable to make a fine adjustmentto this central magnetic field value, for example to reset the centralmagnetic field to the specified value after it has been altered by useof a passive or superconducting shim coil assembly (which is used toachieve the optimum degree of homogeneity within the homogeneity volumebut which can sometimes lead to a slight change in the central magneticfield value). Ideally this fine adjustment should be made without anydegradation of the magnetic field homogeneity within the homogeneityvolume.

It is known to make use of a so-called B0 shim coil assembly to providefine adjustment of the central magnetic field value with minimaldegradation of the magnetic field homogeneity within the homogeneityvolume. Such a B0 shim coil assembly comprises a plurality ofsuperconducting coils connected in series to form a closed loop which iselectrically separate from the main superconducting coil assembly butwhich couples magnetically with the main coil assembly. The B0 shimcoils are wound on an outer former which surrounds an inner former onwhich the main coils are wound and within which the homogeneity volumeis located. The B0 shim coil assembly also incorporates asuperconducting switch within the loop and current input terminals foradjusting the amount of current passing through the shim coils and forenabling persistence of this current when the required current value isreached and the superconducting switch is closed, the required currentvalue being zero or a positive or negative value. The geometries of theB0 shim coils are chosen so as to have substantially no effect on thehomogeneity of the magnetic field within the homogeneity volume.Furthermore the B0 shim coils are constructed using materials such thatthe maximum required operating current is well below the criticalcurrent at which the coils are no longer superconducting and such thatthere is insignificant drift in the magnetic fields associated withthese coils. Thus, in the persisted mode in which the uniform centralmagnetic field is maintained within the homogeneity volume, the currentin the shim coils will remain substantially unchanged ignoring theeffect of any inductive interactions with any other part of theelectromagnet apparatus or with any external field source. Typically theshim coils are constructed using wire having a critical current of thesame order of magnitude as the wire used for the main magnet coils.

In most circumstances the coupling of the B0 shim coil assembly withother shim coil assemblies, which are provided to correct distortions inthe magnetic field due to other disturbing influences, is minimal. Thiscan be ensured by appropriate choice of the shim coil geometries. As iswell known the superconducting switch of the B0 shim coil assembly canbe operated in the same manner as the superconducting switch which isprovided for controlling the main coil assembly. In both cases, afterthe coils have been charged to the required current level from anexternal current source whilst the loop is open-circuited by opening ofthe switch, the switch is closed to allow the required constant currentlevel to be maintained within the superconducting loop incorporating thecoils. Where the main coil assembly is being initially energised, suchswitching of the switches associated with the main coil assembly and theB0 shim coil assembly can be effected in series. However, when the maincoil assembly is in the persisted mode, switching of the B0 shim coilassembly must be effected independently of the main coil assembly toprovide the required fine adjustment of the central magnetic field.

In addition to the ability to set the central magnetic field to aprecise desired value, it is important in many applications that thisset value remains stable with time. For example, in NMR spectroscopy,experiments conducted within the apparatus can last over several daysand even small variations in the value of the central magnetic field,for example of the order of a few parts per billion, can lead tosystematic differences in the spectral results obtained as a result ofsuch experiments. There are essentially two ways in which the centralmagnetic field value can exhibit time-dependence, that is either as aresult of a change in the ambient magnetic field due to externalsources, or as a result of variation in the magnetic field generated bythe main coil assembly itself.

WO 89/09475 discloses a superconducting electromagnet apparatus whichmakes use of an assembly of auxiliary coils which magnetically couple tothe main coil assembly in order to reduce the effect of variation of thecentral magnetic field value due to changes in the ambient magneticfield. In such apparatus an assembly of superconducting shielding coilsconnected in series within a loop is arranged so that the effectiveareas and mutual and self inductances of the main coils and theshielding coils are such that any change in the ambient magnetic fieldcauses changes in the currents of the main coils and the shielding coilsin such a manner as to generate a change in the central magnetic fieldwhich opposes the change in the central magnetic field due to the changein the ambient magnetic field alone. The main coil assembly would itselfusually partially shield the homogeneity volume from the effect of suchchanges in the ambient magnetic field even without the use of suchshielding coils, but the shielding effect can be significantly increasedby the use of the shielding coils.

Furthermore EP 0468425A discloses an active-shield superconductingelectromagnet apparatus comprising a first superconducting coil assemblyfor generating a first magnetic field, and a second superconducting coilassembly for generating a second magnetic field, the second coilassembly being electrically connected in series with the first coilassembly and the two assemblies being arranged such that a resultant,uniform magnetic field is generated in the working volume and the secondmagnetic field opposes the first magnetic field externally of theapparatus so that the stray magnetic field outside the coil assembliesis very small. This enables personnel to work safely relatively close tothe apparatus without requiring an excessive amount of cumbersome andexpensive iron shielding.

However the automatic shielding arrangement of WO 89/09475 is no longereffective in relation to conventional active-shield superconductingelectromagnet apparatus. Accordingly EP 0468425A proposes an arrangementin which screening coils connected within a closed loop are providedhaving a number of turns at least an order of magnitude less than thenumber of turns in the first and second coil assemblies so as to reducethe effect of disturbing influences on the central magnetic field whilsthaving an insignificant effect on the homogeneity of the centralmagnetic field. In this case the screening coils are wound fromsuperconducting wire having a critical current such that they revert tothe normal conducting state during quenching of the first and secondcoil assemblies. In this way the maximum contribution which thescreening coils can make to the stray magnetic field is renderedinsignificant. Furthermore the number of turns of the screening coils isso small that it is a straightforward matter to generate current in thescreening coils to provide adequate screening capacity without risk ofgenerating significant stray magnetic field.

With regard to the second effect producing variation of the centralmagnetic field value over time, that is variation of the magnetic fieldgenerated by the main coil assembly itself as a result of variation ofthe current supplied to the coil assembly, this effect can be caused bythe properties of the superconducting wire which is used to wind thecoils and which can result in a very slow decrease in the current(typically several parts per billion per hour of the operating currentvalue) in a phenomenon known as “drift”. It is possible to model suchdrift in terms of an effective residual resistance of the main coils,and to compensate for the drift on the basis of this relationship. Thecompensating of drift in this way is referred to as “locking”. However,in order for such compensation to be effective, it is important that thedrift of the current in the compensating coils is insignificant bycomparison with the drift of the current in the main coils. Since theeffective residual resistance increases significantly as the operatingcurrent in the coils becomes comparable with the critical current valueof the wire used for winding the coils, this requires the criticalcurrent value for a given maximum current in the compensating coils tobe greater than a particular minimum value.

Furthermore the conventional B0 shim coil assembly as described aboveactually has the effect of increasing the rate of change of the centralfield due to the drift of the current in the main coil assembly.

It is an object of the invention to provide superconductingelectromagnet apparatus with a B0 shim coil assembly which, as well asproviding fine adjustment of the central magnetic field value, alsocompensates for changes in the central magnetic field value with timeeither as a result of changes in the ambient magnetic field or as aresult of changes in the field generated by the main coil assemblyitself, or as a result of both such effects.

BRIEF SUMMARY OF THE INVENTION

According to the present invention there is provided superconductingelectromagnet apparatus comprising a main coil assembly (1; 1′) forproducing a central magnetic field in a working volume, main currentsupply means (5) connected to the main coil assembly for energising andde-energising the main coil assembly, and for persisting thesuperconducting current flow in the main coil assembly when a desiredconstant current level has been reached, in order to generate a centralmagnetic field of high homogeneity in the working volume, a B0 shim coilassembly (2; 2′) for providing fine adjustment of the central magneticfield, the B0 shim coil assembly comprising superconducting shim coilmeans connected within a closed loop and arranged to magnetically couplewith the main coil assembly (1; 1′), auxiliary current supply means (6)connected to the B0 shim coil assembly for supplying current to theclosed loop, and for persisting the superconducting current flow in theclosed loop when a desired constant current level has been reached, inorder to provide fine adjustment of the central magnetic field withinthe working volume without significantly degrading the homogeneity ofthe central magnetic field, and control means (31, 38) for controllingthe main and auxiliary current supply means (5, 6), wherein the maincoil assembly (1; 1′), the B0 shim coil assembly (2; 2′) and the controlmeans (31, 38) are adapted to provide significant compensation for theeffect of variation of the magnetic field within the working volume withtime whilst maintaining the superconducting current flows in the maincoil assembly (1; 1′) and the B0 shim coil assembly (2; 2′).

It should be understood that the term “significant compensation” is usedin this context to denote a level of compensation which is such as tolead to a significant improvement in system performance. This wouldinclude situations where an experiment or application is achievable withsuch “significant compensation”, whereas such an experiment orapplication could not be performed without such compensation.

It will be appreciated that the invention provides an arrangement bywhich a single closed loop coil assembly can perform the function of aB0 shim whilst at the same time compensating for the effect of variationof the magnetic field within the working volume with time. The coilassembly may be adapted to compensate for the effect of time variationof the magnetic field as a result of time variation of the ambientmagnetic field, or alternatively may be adapted to compensate for theeffect of time variation of the magnetic field as a result of drift ofthe current in the main coil assembly. As a further alternative the shimcoil assembly may be adapted to compensate for both of thesetime-varying effects. However in all cases the single closed loop coilassembly serves several functions, and thus avoids the need to provideindividual closed loop coil assemblies for performing these functionsseparately which would result in functional difficulties in view of thefact that each such auxiliary coil assembly would couple inductivelywith the other auxiliary coil assemblies as well as with the main coilassembly. Furthermore the provision of separate auxiliary coilassemblies for performing the different functions individually wouldresult in additional complications in the design and construction of theapparatus, as well as rendering the apparatus more expensive thanapparatus in accordance with the invention in which a single closed loopcoil assembly is adapted to perform more than one functionsimultaneously, that is the above-described shielding and/or lockingfunctions in addition to the fine adjustment of the central magneticfield value.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

In order that the invention may be more fully understood,superconducting electromagnet apparatus in accordance with the inventionwill now be described, by way of example, with reference to theaccompanying drawings, in which:

FIG. 1 is a schematic diagram of a first embodiment of the invention;

FIG. 2 is a further schematic diagram showing the positions and sizes ofindividual coils within the first embodiment;

FIG. 3 is a block diagram of a control system for such apparatus; and

FIGS. 4 and 5 are schematic diagrams of a second embodiment of theinvention.

DETAILED DESCRIPTION OF THE INVENTION

A description will now be given of a particular form of superconductingelectromagnet apparatus in accordance with the invention for use in aparticular NMR spectroscopy application in which a central magneticfield of high homogeneity and high constancy with respect to time isgenerated. However it should be appreciated that the design of suchapparatus is dictated by the particular application in which it is to beused, and that different designs of apparatus in accordance with theinvention are required for other applications. Furthermore thedescription of such apparatus omits a description of those featureswhich are already well known in the art, such as the particular methodof fabrication of the coils and details of the associated radiationshielding and cooling arrangements.

Referring to FIG. 1 the superconducting electromagnet apparatuscomprises a cylindrical main coil assembly consisting of main coils 1connected in series within a closed loop 1 a including a superconductingswitch 3 having a heating element and electrical connections 5 for thesupply of drive current to the main coils from an external currentsource (not shown). The superconducting switch 3 is also provided withelectrical connections 7 for the supply of current to the heatingelement of the switch 3. Furthermore a B0 shim coil assembly is providedin the form of B0 shim coils 2 connected in series within a closed loop2 a including a superconducting switch 4 having a heating element andelectrical connections 6 for supply of drive current to the B0 shimcoils from an external current source (not shown). The superconductingswitch 4 is also provided with electrical connections 8 for the supplyof current to the heating element of the switch 4.

FIG. 2 diagrammatically shows an upper axial section through theapparatus. It will be appreciated that the lower axial section is notshown in order to render the figure easier to read, but that this issimilar to the upper axial section, and that in practice each of thecoils and formers shown in the figure are of cylindrical formsurrounding an axial bore 9 defining the working volume of the magnet.Referring to FIG. 2 the main coil assembly comprises two main magnetcoils 11 and 12 wound on an inner cylindrical aluminium former 10 (shownin broken lines in the figure). The current circulating through the twomain magnet coils 11 and 12 provides most of the central magnetic field,but the magnetic field produced by these coils would not be homogeneousenough for NMR spectroscopy applications without the provision offurther compensating coils. Accordingly smaller compensating coils 13,14, 15 and 16 are wound on a further cylindrical aluminium former 20(also shown in broken lines in the figure) which is coaxial with, andsurrounds, the inner former 10. The purpose of the smaller compensatingcoils 13 to 16 is to correct for most of the lowest order axialinhomogeneities introduced by the main magnet coils 11 and 12. The coils11 to 16 are connected in series within a closed loop and are suppliedwith current in a manner already described above.

The design of the B0 shim coil assembly follows broadly similarprinciples to ensure that it produces a largely homogeneous centralmagnetic field contribution within the homogeneity volume. To this endthe B0 shim coil assembly comprises a long solenoid coil 17 wound on theinner former 10 between the coils 11 and 12, and two smaller coils 18and 19 wound on top of the coils 13 and 14 on the former 20 and designedto substantially cancel the lowest order inhomogeneities that would beproduced by the coil 17 alone. The coils 17, 18 and 19 are connected inseries within a closed loop and are supplied with current in a manneralready described above. The positions of the coils 17, 18 and 19, andthe numbers of turns in each coil, are chosen so that the effective B0strength is suitable for the specific application and such as to producefavourable locking and shielding effects. In particular the central coil17 should be positioned close to the working volume in order to providethe required locking effect. It should be noted that, since the centralcoil 17 is wound on the same former 10 as the main coils 11 and 12, thethree coils are potted together, that is embedded within the sameintegral block of wax or other potting material. An outer former 30(also shown in broken lines in the figure) is provided for the other(conventional) superconducting shim coils 29 for optimising thehomogeneity of the central magnetic field within the homogeneity volume.

FIG. 3 shows a block circuit diagram of the current supply and controlsystem for such apparatus. A power supply 31 is provided for supplyingand controlling current to the B0 shim coil assembly 32, andadditionally for controlling the supply of current from a current source34 to the heating element of the superconducting switch 33 of the B0shim coil assembly. Furthermore a power supply 38 is provided for thesupply and control of current to the main coil assembly 35, as well asfor controlling the supply of current from a current source 32 to theheating element of the superconducting switch 36 of the main coilassembly.

When the main magnet switch 36 is opened, the B0 shim coil switch 33 isalso normally held open, the ability to control the current sources 37and 34 serially being indicated schematically by an arrow connecting thesource 37 to the source 34. In one possible arrangement the B0 shim coilswitch 33 opens automatically if the main magnet develops a voltageacross it above a certain threshold, for example in quench conditions orif the main coil switch 36 is open. This protects the B0 shim coilassembly 32 from damage which might otherwise result from the largecurrent produced by inductive coupling to the main coil assembly 35 ifthe main coil assembly were to quench or the main coil switch were toopen. It is also possible to control the B0 shim coil switchindependently of the power supply 31 as shown by the arrow 39.

The specific coil geometry for both the main coil assembly and the B0shim coil assembly in a particular example is indicated in Table 1below. From this geometry, the effective areas for the two circuits canbe calculated, and in turn the current/field ratios and the self andmutual inductances can be derived. These are given in Table 2 below.Using these parameters in equations 4, 6 and 10 of the theoreticalsummary set out below yields an effective B0 strength of 1.4 mT/A, ashielding factor to external influences of approximately 6, and alocking factor for central magnetic field drift of approximately 6.7.

TABLE 1 Geometry of particular example coil mean radius (cm) width (cm)turns 11 4.58 33.00   7330 12 5.76 33.00  21146 13 7.17 4.70  1066 147.03 0.20   18 15 7.17 4.70  1066 16 7.03 0.20   18 17 5.01 33.00   366218 7.43 4.70  103 19 7.43 4.70  103

TABLE 2 Calculated parameters of particular example Mutual inductance ofmain magnet and B0 2.98 H Self inductance of main magnet 25.88 H Selfinductance of B0 shim 0.3892 H Effective area of main magnet 307.3 m²Effective area of B0 shim 32.4 m² Strength of main magnet 1.06E−01 T/AStrength of B0 shim alone 1.36E−02 T/A

It should be appreciated that various modifications of this basic designare possible within the scope of the invention. For example the maincoil assembly may include coils wound in either sense and may comprise amixture of coils with some of the coils being wound in one direction andother coils being wound in the opposite direction. In particular themain coil assembly may be arranged to provide active screening asdescribed above. Furthermore the B0 shim coil assembly may also includecoils wound in either sense and may comprise a mixture of coils wound inone direction and coils wound in the opposite direction.

Although the B0 shim coils 17, 18 and 19 are described as separatelywound coils in the description with reference to FIG. 2, it should beappreciated that it would also be possible for some or all of thewindings of the B0 shim coil assembly to be constituted by parts of themain coil assembly, so that these parts of the main coil assembly wouldform parts of both the main magnet circuit and the B0 shim coil circuitand would carry current from both circuits. The incorporation of all orpart of the B0 shim coil assembly in the main coil assembly may beadvantageous in certain circumstances, and may provide a simpler andless costly construction.

FIG. 4 is a diagram, similar to that of FIG. 1, showing a secondembodiment of the invention in which the B0 shim coils 2′ areconstituted by parts of the main coils 1′. In FIG. 4 like referencenumerals denote the same parts as in FIG. 1. Furthermore FIG. 5diagrammatically shows the connections between the coils in this secondembodiment in more detail, the coils consisting of two main magnet coils11′ and 12′, smaller compensating coils 13′, 14′, 15′ and 16′ and the B0shim coils 17, 18′ and 19′ having similar functions to the correspondingcoils 11-19 shown in FIG. 2. Apart from the fact that the B0 shim coils17, 18 and 19 form parts of the main coil assembly, the construction ofthis second embodiment is similar to that of the first embodiment.

Theoretical Basis

The following description provides what is believed to be a reasonabletheoretical basis for the design of superconducting electromagnetapparatus in accordance with the invention in which a single coilassembly performs the three functions of a B0 shim, shielding andlocking.

The main properties of a combined B0 shin/shielding/locking coilassembly can be deduced from three basic equations governing the mainmagnet/shim interactions. Equations 1 and 2 represent Faraday's law ofinduction applied to the main coil assembly and shim coil assemblyrespectively, and equation 3 is related to Ampère's law.${1.\quad - \frac{\varphi_{m}}{t}} = {{A_{m}\frac{B_{ext}}{t}} = {{{- L_{m}}\frac{I_{m}}{t}} - {M\frac{I_{s}}{t}} + {I_{m}R_{m}}}}$${2.\quad - \frac{\varphi_{s}}{t}} = {{A_{s}\frac{B_{est}}{t}} = {{{- L_{s}}\frac{I_{s}}{t}} - {M\frac{I_{m}}{t}} + {I_{s}R_{s}} + ɛ_{s}}}$${3.\quad \frac{B}{t}} = {{S_{m}\frac{I_{m}}{t}} + {S_{s}\frac{I_{s}}{t}} + \frac{B_{ext}}{t}}$

In these equations the symbols represent the following:

Symbol Meaning A_(m) Effective area of main coil assembly A_(s)Effective area of B0 shim coil assembly B Central magnetic field B_(ext)External (ambient) magnetic field ε_(s) Applied emf when adjusting B0current I_(m) Current in main coil assembly I_(s) Current in B0 shimcoil assembly L_(m) Self inductance of main coil assembly Ls Selfinductance of B0 shim coil assembly M Mutual inductance of main/B0 shimcoil assemblies φ_(m) Flux linking main coil assembly φ_(s) Flux linkingB0 shim coil assembly R_(m) Effective residual resistance of main coilassembly R_(s) Effective residual resistance of B0 shim coil assemblyS_(m) Central magnetic field/current ratio for isolated main coilassembly S_(s) Central magnetic field/current ratio for isolated B0 shimcoil assembly

A) If current is driven into the B0 shim coil assembly at a rate muchfaster than any external field changes and any internal magnet drift(i.e. in all practical cases), equation 1 gives ΔI_(m)=−(M/L_(m))ΔI_(s),which in equation 3 leads to an effective B0 strength of:${{4.\quad S_{B_{0}}} \cong \frac{\Delta \quad B}{\Delta \quad I_{s}}} = {S_{s} - {\frac{M}{L_{m}}{S_{m}.}}}$

The first term on the right-hand side of this equation is the change inthe central magnetic field per amp for the isolated B0 shim coilassembly, and the second term is the effect on the central magneticfield due to the induced change in current in the main coil assembly peramp of current in the B0 shim coil assembly.

B) If the B0 shim coil assembly is in the persisted state but there areperturbations in the ambient magnetic field (dB_(ext)/dt≠0) whichdominate compared to the drift of the magnet, then solving equations 1and 2 gives:${5.\quad \Delta \quad I_{s}} = {\frac{{MA}_{m} - {L_{m}A_{s}}}{{L_{m}L_{s}} - M^{2}}\Delta \quad B_{ext}}$$\quad {{\Delta \quad I_{m}} = {\frac{{MA}_{s} - {L_{s}A_{m}}}{{L_{m}L_{s}} - M^{2}}\Delta \quad {B_{ext}.}}}$

By using equations 5 in 3, the reduction in the influence of a change inthe ambient magnetic field can be shown to be:${6.\quad \frac{\Delta \quad B_{est}}{\Delta \quad B}} = {\left\lbrack {1 + \frac{{\left( {{MA}_{m} - {L_{m}A_{s}}} \right)S_{s}} + {\left( {{MA}_{s} - {L_{s}A_{m}}} \right)S_{m}}}{{L_{m}L_{s}} - M^{2}}} \right\rbrack^{- 1}.}$

The first term on the right-hand side of this equation (unity) is thechange in the central magnetic field with neither the main coil assemblynor the B0 shim coil assembly present. Furthermore the first part of thesecond term is the change in the central magnetic field due to thecurrent induced in the B0 shim coil assembly considered as part of thecomplete system, that is allowing for inductive coupling with the maincoil assembly. The second part of the second term is the change in thecentral magnetic field due to the current induced in the main coilassembly considered as part of the complete system, that is allowing forinductive coupling with the main coil assembly.

C) If the main coil assembly is in the persisted state but there are noexternal perturbations to the magnetic field, then the natural magnetdrift (allowed for in equations 1 and 2 by the effective resistances)will become dominant. If the B0 shim coil assembly is designed such thatI_(s)<<I_(c) (critical current), then we can assume that R_(s)≈0, andequation 2 can be substituted in equation 1 to give:${7.\quad \frac{1}{I_{m}}\frac{I_{m}}{t}} = {\left( {\frac{M^{2}}{L_{s}} - L_{m}} \right)^{- 1}R_{m}}$

From this, the change in the magnetic field is found from equation 3:${8.\quad \frac{B}{t}} = \frac{I_{m}{R_{m}\left( {S_{m} - {S_{s}\frac{M}{L_{s}}}} \right)}}{\left( {\frac{M^{2}}{L_{s}} - L_{m}} \right)}$

Without the B0 shim coil assembly the main magnet drift would be:${{9.\quad \frac{B_{m}}{t}} = {I_{m}S_{m} \times {- \frac{R_{m}}{L_{m}}}}},$

so that the reduction in magnetic field change is given by:${10.\quad \frac{\Delta \quad B_{m}}{\Delta \quad B}} = {\frac{\left( {1 - \frac{M^{2}}{L_{m}L_{s}}} \right)}{\left( {1 - {\frac{S_{s}}{S_{m}}\frac{M}{L_{s}}}} \right)}.}$

The denominator on the right-hand side of this equation relates to thechange in the central magnetic field due to the current inductivelycoupled into the B0 shim coil assembly relative to the change in thecentral magnetic field due to the current inductively coupled out of themain coil assembly. The numerator relates to the effect which theinductive coupling of the two coil assemblies has on the rate of changeof current in the main coil assembly.

It will be appreciated that equations 4, 6 and 10 above can be appliedto determine the optimum geometries and positioning of the main coilassembly and B0 shim coil assembly in order to provide the requiredlocking and/or shielding in addition to the conventional B0 shimfunction of the B0 shim coil assembly. The effect of moving a coil (thecoil 17 in FIG. 2) of the B0 shim coil assembly further towards themagnet bore is to increase S_(s) but to decrease A_(s), and this canresult in an increase in the locking effect, although in some cases itcan also lead to a decrease in the shielding effect.

What is claimed is:
 1. A superconducting electromagnet apparatuscomprising a main coil assembly (1; 1′) for producing a central magneticfield in a working volume, main current supply means (5) connected tothe main coil assembly for energising and de-energising the main coilassembly, and for persisting the superconducting current flow in themain coil assembly when a desired constant current level has beenreached, in order to generate a central magnetic field of highhomogeneity in the working volume, a B0 shim coil assembly (2; 2′) forproviding fine adjustment of the central magnetic field (B0 being themagnetic field along a central axis), the B0 shim coil assemblycomprising superconducting shim coil means connected within a closedloop and arranged to magnetically couple with the main coil assembly (1;1′), auxiliary current supply means (6) connected to the B0 shim coilassembly for supplying current to the closed loop, and for persistingthe superconducting current flow in the closed loop when a desiredconstant current level has been reached, in order to provide fineadjustment of the central magnetic field within the working volumewithout significantly degrading the homogeneity of the central magneticfield, and control means (31, 38) for controlling the main and auxiliarycurrent supply means (5, 6), wherein the main coil assembly (1; 1′), theB0 shim coil assembly (2; 2′) and the control means (31, 38) providesignificant compensation, resulting in a sustained improvement inperformance, for the effect of variation of the magnetic field withinthe working volume with time whilst the current flow in the main coilassembly (1; 1′) and the B0 shim coil assembly (2; 2′) remainssuperconducting.
 2. Apparatus according to claim 1, wherein the maincoil assembly (1; 1′), the B0 shim coil assembly (2; 2′) and the controlmeans (31, 38) are adapted to compensate for the effect of timevariation of the magnetic field within the working volume as a result ofvariation of the ambient magnetic field with time.
 3. Apparatusaccording to claim 1, wherein the main coil assembly (1; 1′), the B0shim coil assembly (2; 2′) and the control means (31, 38) are adapted tocompensate for the effect of time variation of the magnetic field withinthe working volume as a result of variation of the current flow in themain coil assembly with time.
 4. Apparatus according to claim 1, whereinthe B0 shim coil assembly (2; 2′) is constructed from a material havinga critical current value, at which the B0 shim coil assembly wouldrevert to the normal conducting state, which is significantly greaterthan the value of the current required to compensate for time variationof the magnetic field within the working volume.
 5. Apparatus accordingto claim 1, wherein the B0 shim coil assembly (2; 2′) incorporates atleast one coil wound on the same former as at least one coil of the maincoil assembly.
 6. Apparatus according to claim 1, wherein the auxiliarycurrent supply means (6) incorporates a superconducting switch (4)including a heating element for heating the switch (4) to drive it outof its superconducting state to cause the current passing through theswitch (4) to decay.
 7. Apparatus according to claim 1, wherein the maincurrent supply means (5) incorporates a superconducting switch (3)including a heating element for heating the switch (3) to drive it outof its superconducting state to cause the current in the main coilassembly (1; 1′) to decay.
 8. Apparatus according to claim 1, whereinthe auxiliary current supply means (6) includes input terminals to whichcurrent is supplied under control of the control means (31) duringinitial energisation of the B0 shim coil assembly (2; 2′), such currentsupply to the input terminals being terminated when the current flowingin the closed loop has reached the desired level.
 9. Apparatus accordingto claim 1, wherein the main coil assembly (1; 1′) comprises a pluralityof superconducting main coils connected in series within a closed loop.10. Apparatus according to claim 1, wherein the main coil assembly (1;1′) comprises at least one coil wound in one direction and at least oneother coil wound in the opposite direction.
 11. Apparatus according toclaim 1, wherein the B0 shim coil assembly (2; 2′) comprises a pluralityof superconducting shim coils connected in series within a closed loop.12. Apparatus according to claim 11, wherein at least one of the coilsof the B0 shim coil assembly (2; 2′) is constituted by part of the maincoil assembly.
 13. Apparatus according to claim 1, wherein the B0 shimcoil assembly (2; 2′) comprises at least one coil wound in one directionand at least one other coil wound in the opposite direction. 14.Apparatus according to claim 1, wherein at least one further shim coilassembly (29) is provided for adjustment of the degree of homogeneity ofthe central magnetic field.